Do you receive messages sent to you when you cut your service back on (iPhone, at&t)?

My iphone was stolen and the phone was disposed of… So I'm getting a new iphone, same model(5s) and I wanted to know that when I get the service cut back on with my new phone, will I receive any messages sent to me over the past few months?

If you are keeping the same number and same apple id than maybe but the phone is disposed so it is no big deal if it shows.